The body was found Wednesday morning at a construction site near Children's Memorial Hermann Hospital.
Stanley Spigel, 73, was described by his family as a husband, father and successful business man.
A member of his extended family said that he had been depressed for the past few months.
Spigel was a patient at Methodist Hospital, and was waiting for an ambulance to transfer him to the Menninger Clinic before his disappearance.
"He was at Houston Methodist and was supposed to be picked up by ambulance, and the ambulance was late. So he just vanished," said Jack Zimmermann, who is related to the Spigel family.
The hospital's security alert was sent out after Spigel disappeared.
The alert stated that Spigel had left the Walter Tower building, exited the stairwell, and walked towards the intersection on Bertner and John Freeman.
A tweet from HPD stated that, "Foul play was suspected. The body found was that of an elderly white male with blunt force trauma to his head."
The medical examiner's office is working to determine if the death was a homicide.